(i) The probability that both sweets are toffees is calculated by considering each box separately and then summing the probabilities:

For Box A: \(\frac{1}{3} \times \frac{6}{10} \times \frac{5}{9}\)

For Box B: \(\frac{1}{3} \times \frac{5}{8} \times \frac{4}{7}\)

For Box C: \(\frac{1}{3} \times \frac{3}{10} \times \frac{2}{9}\)

Summing these probabilities gives:

\(\frac{1}{3} \times \frac{6}{10} \times \frac{5}{9} + \frac{1}{3} \times \frac{5}{8} \times \frac{4}{7} + \frac{1}{3} \times \frac{3}{10} \times \frac{2}{9} = \frac{53}{210} \approx 0.252\)

(ii) Given that both sweets are toffees, the probability that they came from Box A is calculated using conditional probability:

\(P(A \mid \text{TT}) = \frac{P(A \cap \text{TT})}{P(\text{TT})} = \frac{0.111}{0.252} = \frac{70}{159} \approx 0.440\)